Preface.
1 What Do Engineers Do?
2 Miscellaneous Math Skills.
2.1 Equations of Lines, Planes, and Circles.
2.2 Areas and Volumes of Common Shapes.
2.3 Roots of a Quadratic Equation.
2.4 Logarithms.
2.5 Reduction of Fractions and Lowest Common Denominators.
2.6 Long Division.
2.7 Trigonometry.
2.7.1 The Common Trigonometric Functions: Sine, Cosine, and
Tangent.
2.7.2 Areas of Triangles.
2.7.3 The Hyperbolic Trigonometric Functions: Sinh, Cosh, and
Tanh.
2.8 Complex Numbers and Algebra, and Euler?s Identity.
2.8.1 Solution of Differential Equations Having Sinusoidal
Forcing Functions.
2.9 Common Derivatives and Their Interpretation.
2.10 Common Integrals and Their Interpretation.
2.11 Numerical Integration.
3 Solution of Simultaneous, Linear, Algebraic
Equations.
3.1 How to Identify Simultaneous, Linear, Algebraic
Equations.
3.2 The Meaning of a Solution.
3.3 Cramer?s Rule and Symbolic Equations.
3.4 Gauss Elimination.
3.5 Matrix Algebra.
4 Solution of Linear, Constant-Coeffi cient, Ordinary
Differential Equations.
4.1 How to Identify Linear, Constant-Coeffi cient, Ordinary
Differential Equations.
4.2 Where They Arise: The Meaning of a Solution.
4.3 Solution of First-Order Equations.
4.3.1 The Homogeneous Solution.
4.3.2 The Forced Solution for ?Nice?
f(t).
4.3.3 The Total Solution.
4.3.4 A Special Case.
4.4 Solution of Second-Order Equations.
4.4.1 The Homogeneous Solution.
4.4.2 The Forced Solution for ?Nice?
f(t).
4.4.3 The Total Solution.
4.4.4 A Special Case.
4.5 Stability of the Solution.
4.6 Solution of Simultaneous Sets of Ordinary Differential
Equations with the Differential Operator.
4.6.1 Using the Differential Operator to Verify Solutions.
4.7 Numerical (Computer) Solutions.
5 Solution of Linear, Constant-Coeffi cient, Difference
Equations.
5.1 Where Difference Equations Arise.
5.2 How to Identify Linear, Constant-Coeffi cient Difference
Equations.
5.3 Solution of First-Order Equations.
5.3.1 The Homogeneous Solution.
5.3.2 The Forced Solution for ?Nice?
f(n).
5.3.3 The Total Solution.
5.3.4 A Special Case.
5.4 Solution of Second-Order Equations.
5.4.1 The Homogeneous Solution.
5.4.2 The Forced Solution for ?Nice?
f(n).
5.4.3 The Total Solution.
5.4.4 A Special Case.
5.5 Stability of the Solution.
5.6 Solution of Simultaneous Sets of Difference Equations with
the Difference Operator.
5.6.1 Using the Difference Operator to Verify Solutions.
6 Solution of Linear, Constant-Coeffi cient, Partial
Differential Equations.
6.1 Common Engineering Partial Differential Equations.
6.2 The Linear, Constant-Coeffi cient, Partial Differential
Equation.
6.3 The Method of Separation of Variables.
6.4 Boundary Conditions and Initial Conditions.
6.5 Numerical (Computer) Solutions via Finite Differences:
Conversion to Difference Equations.
7 The Fourier Series and Fourier Transform.
7.1 Periodic Functions.
7.2 The Fourier Series.
7.3 The Fourier Transform.
8 The Laplace Transform.
8.1 Transforms of Important Functions.
8.2 Useful Transform Properties.
8.3 Transforming Differential Equations.
8.4 Obtaining the Inverse Transform Using Partial Fraction
Expansions.
9 Mathematics of Vectors.
9.1 Vectors and Coordinate Systems.
9.2 The Line Integral.
9.3 The Surface Integral.
9.4 Divergence.
9.4.1 The Divergence Theorem.
9.5 Curl.
9.5.1 Stokes? Theorem.
9.6 The Gradient of a Scalar Field.
Index.